Bi-level iso-surface compression

ABSTRACT

Methods, structures and systems for encoding and decoding isosurface data. An encoder process takes volume data and an isolevel as input and produces compressed isosurface data as output. The compressed isosurface data produced by an encoder process is composed of an occupancy image record, an optional intersection points record, and an optional normal vectors record. An occupancy image is compressed with a context-based arithmetic encoder. Compressed isosurface data can be stored in a data storage device or transmitted through a communication medium to a remote computer system, where the decoder process is executed. The decoder processes take compressed surface data as input and produce surface data as output. The decoder processes first reconstructs the occupancy image by decoding the occupancy image record. An in-core isosurface decoder process produces a polygon mesh as a surface representation. An out-of-core isosurface decoder process produces a set of oriented points as a surface representation.

PRIORITY

This application claims priority to a Provisional Application, havingthe same title, assigned, Ser. No. 60/400,202, and filed Jul. 31, 2002,which is incorporated herein by reference in its entirety for allpurposes.

FIELD OF THE INVENTION

This invention relates to the fields of computer graphics and scientificvisualization. It is more particularly related to representingisosurface data in compressed form, especially suitable for compactstorage and fast transmission, and remote visualization.

BACKGROUND OF THE INVENTION

Polygon meshes are widely used in computer aided geometric design,geometric modeling, medical imaging, and computer graphics to representsurfaces in digital form. Polygon meshes are described in detail in U.S.Pat. No. 5,506,947 “Curve and Surface Smoothing Without Shrinkage,” byG. Taubin, and in the paper “A Signal Processing Approach To FairSurface Design,” by G. Taubin, Siggraph'95 Conference Proceedings,August 1995, pages 351-358, both are incorporated herein by reference inits entirety for all purposes. A polygon mesh includes a polygon meshconnectivity, a set of polygon mesh vertex positions, and a set ofpolygon mesh normals. The polygon mesh connectivity includes a pluralityof vertices, and a plurality of faces. The set of polygon mesh vertexpositions includes a plurality of vertex position vectors, with eachvertex position vector corresponding to one vertex of the polygon meshconnectivity. The set of polygon mesh normals can be either a set ofpolygon mesh vertex normals or a set of polygon mesh face normals. Theset of polygon mesh vertex normals includes either a plurality of vertexnormals, with each vertex normal corresponding to one vertex of thepolygon mesh connectivity. The set of polygon mesh face normals includeseither a plurality of face normals, with each face normal correspondingto one face of the polygon mesh connectivity.

An isosurface extraction algorithm constructs a polygon meshapproximation of a level.set of a scalar function defined in the volumespanned by a 3D regular grid. Data acquired by medical imaging systemssuch as Computed Axial Tomography (CAT) Scanners and Magnetic ResonanceImaging (MRI) Scanners are example of scalar functions defined on thevertices of a 3D regular grid. The 3D regular grid includes a pluralityof grid vertices and a plurality of grid edges, with each grid edgeconnecting two particular grid vertices. Two grid vertices connected bya grid edge are called neighbors. The grid vertices of the 3D regulargrid are points p_(α) in 3D space, where α=(α₀,α₁,α₂) is a triple ofnon-negative integers, α₀ε{0, . . . ,n₀−1}, α₁ε{0, . . . ,n₁−1}, α₂ε{0,. . . ,n₂−1}. FIG. 1 is a prior art diagram showing a 3D regular grid100 and one of its cells 140. The grid vertices of the 3D regular gridare organized as n₀ layers 110, n₁ rows 120, and n₂ columns 130. Eachset of eight neighboring grid vertices form a cell 140C _(α) ={p _(α) ,p _(α−(001)) ,p _(α−(010)) ,p _(α−(011)) ,p _(α−(100),)p _(α−(101)) ,p _(α−(110)) ,p _(α−(111))}The cells of the 3D regular grid correspond to values of α=(α₀,α₁,α₂) inthe following ranges: α₀ε{1, . . . ,n₀−1}, α₁ε{1, . . . ,n₁−1}, α₂ε{1, .. . ,n₂−1}. The vertices of cell 140 are grid vertices 141, 142, 143,144, 145, 146, 147, and 148.

The scalar function f(p) is specified by its values f_(α)=f(p_(α)) onthe grid vertices p_(α) of a 3D regular grid, and by a method tointerpolate in between these values. The level set is specified by anisovalue f₀. The interpolation scheme is assumed to be linear along thegrid edges, so that the isosurface cuts each edge in no more than onepoint. Ifp_(α) and p_(α−δ) ₁are grid points connected by an edge, andf_(α)>f₀>f_(α−δ) ₁ or f_(α)<f₀<f_(α−δ) ₁ ,the location of the point p_(α,j)where the isosurface intersects the edge is given by the formula

$p_{\alpha,j} = {{{\left( {1 - t_{\alpha,j}} \right)p_{\beta}} + {t_{\alpha,j}p_{\alpha}\mspace{20mu}{where}\mspace{14mu} t_{\alpha,j}}} = \frac{f_{\beta} - f_{0}}{f_{\beta} - f_{\alpha}}}$

The isosurface extraction algorithm determines interfaces betweenadjacent data values indicating a change in the measured value, and thenmodels the surface with polygonal elements having a vertex position foreach polygon mesh vertex, and a vector normal to the surface at each ofthe vertices, or a face normal to the surface at each polygonal face ofthe polygon mesh. The most popular isosurface algorithms are Cuberille,described by L. S. Chen, G. T. Herman, R. A. Reynolds, and J. K. Udupain the paper “Surface Shading in the Cuberille Environment,” IEEEComputer Graphics and Applications, vol. 5, no. 12, pages 33-42, 1985;and Marching Cubes, described in detail in U.S. Pat. No. 5,166,876“System and Method for Detecting Internal Structures Contained Withinthe Interior Region of a Solid Object,” by H. E. Cline and W. E.Lorensen, and in the paper “Marching Cubes: a High Resolution 3D SurfaceConstruction Algorithm,” Siggraph Conference Proceedings, 1987, by W. E.Lorensen and A. V. Cline. In this disclosure we refer to the polygonmeshes produced by these and related algorithms as isosurface meshes.

In the Marching Cubes method mentioned above the points defined by theintersection of the isosurface with the grid edges are the vertices ofthe polygon mesh. In the Cuberille method mentioned above each of thepoints defined by the intersection of the isosurface with the grid edgescorrespond to one polygon mesh face. In his PhD thesis “Segmentation andSurface-Based Modeling of Objects in Three-Dimensional BiomedicalImages,” New York University, New York, March 1991, A. D. Kalvinobserved that the polygon mesh generated by Marching Cubes is the dualmesh of the quadrilateral mesh generated by the Cuberille algorithm.Each vertex of the grid where the scalar function is specified (theprimal grid) is the centroid of a dual grid cell, or voxel. Every edgeof the primal grid intersects the common face of the two voxelscorresponding to the ends of the edge. The mesh generated by theCuberille algorithm is the regularized (converted to manifold) boundarysurface of the solid defined by the set of voxels corresponding to gridvertices with scalar value above the isovalue. Without regularization,in general this mesh is highly singular (non-manifold). The conversionto manifold requires duplication of vertices and edges, so that in theresulting mesh every edge has exactly two incident faces. Which verticesto duplicate and how to connect the faces can be determined by virtually{\em shrinking} the solid, moving the faces in the direction of theinside. The multiplicity of each dual grid vertex in the regularizedmesh only depends on the local connectivity of the eight incidentvoxels. Again, the regularization can be done by table lookup while thevolume data is being scanned, with a table of size 256.

The vertices of the polygon mesh generated by the Marching Cubes methodare connected forming polygon faces according to the followingprocedure. Since the function value associated with each of the eightcorners of a cell may be either above or below the isovalue (isovaluesequal to grid function values are called singular and should beavoided), there are 256 possible configurations. A polygonization of thevertices within each cell for each one of these configurations is storedin a static lookup table. When symmetries are taken into account, thesize of the table can be reduced quite significantly.

The Cuberille algorithm constructs its isosurface mesh from the sameinformation as the Marching Cubes algorithm. The edge intersections inthe primal mesh specify the location of the face centroids of theCuberille mesh. The location of the cuberille vertices can then becomputed by local averaging, or by using more accurate schemes, such asthose introduced by S. Gibson in the paper “Constrained Elastic SurfaceNets: Generating Smooth Surfaces From Binary Segmented Data,” MedicalImage Computation and Computer Assisted Interventions, ConferenceProceedings, pages 888-898, 1998; and by G. Taubin in the paper “DualMesh Resampling,” Pacific Graphics 2001, Conference Proceedings, Tokyo,Japan, October 2001. The situation is similar for normals. If computedin the server as the gradient of the scalar function at the edgeintersection points, and included in the compressed data, the MarchingCubes decoder will treat them as vertex normals, and the Cuberilledecoder as face normals. T. Moller, R. Machiraju, K. Muller, and R.Yagel discuss different methods to estimate isosurface normals fromvolume data in the paper “A Comparison of Normal Estimation Schemes,”IEEE Visualization'97, Conference Proceedings, pages 19-26, 1997. If thenormals are not included in the compressed data, then it is up to theclient to decide how to estimate them from the vertex coordinates andthe connectivity information. The implication of these observations isthat there is considerable freedom in the implementation of the decoder,making absolutely no changes to the encoder or the compressed bitstream.It is not even necessary for the decoder to produce a polygon mesh asoutput. For visualization purposes, and in particular if normals areincluded in the compressed data, a point-based approach could be veryeffective. One such point based surface representation approach isdescribed by S. Rusinkiewicz and M. Levoy in the paper “Qsplat: AMultiresolution Point Rendering System for Large Meshes,” SiggraphConference Proceedings, 2000. Another related method is described inU.S. Pat. No. 4,719,685 “Dividing Cubes System And Method For TheDisplay Of Surface Structures Contained Within The Interior Region of aSolid Body,” by H. E. Cline, W. E. Lorensen, and S. Ludke.

A number of general purpose polygon mesh compression algorithms havebeen proposed in recent years. M. F. Deering developed a meshcompression scheme for hardware acceleration, described in U.S. Pat. No.5,793,371 “Method and apparatus for geometric compression ofthree-dimensional graphics data,” and U.S. Pat. No. 5,842,004 “Methodand apparatus for decompression of compressed geometricthree-dimensional graphics data.” Other methods to encode theconnectivity of triangle meshes with no loss of information wereintroduced by Taubin and Rossignac in U.S. Pat. No. 5,825,369“Compression of Simple Geometric Models Using Spanning Trees,” and U.S.Pat. No. 5,905,507 “Compression of Geometric Models Using SpanningTrees;” C. Touma and C. Gotsman in U.S. Pat. No. 6,167,159 “TriangleMesh Compression;” J. Rossignac in the paper “Edgebreaker: ConnectivityCompression for Triangular Meshes,” IEEE Transactions on Visualizationand Computer Graphics, vol. 5, no. 1, pp. 47-61, January-March 1999; S.Gumhold in U.S. Pat. No. 6,469,701 “Method for Compressing GraphicalInformation;” and others.

In the Technical Report GIT-GVU-99-36, “Connectivity Compression forIrregular Quadrilateral Meshes,” Georgia Tech GVU, 1999, A. King, D.Szymczak and J. Rossignac describe a method to compress quadrilateralmeshes. Methods to encode the connectivity of polygon meshes composed offaces with arbitrary number of cerners were introduced by M. Isenburgand J. Snoeyink in the paper “Face fixer: Compressing Polygon Mesheswith Properties,” Siggraph 2000 Conference Proceedings, pages 263-270,July 2000; B. Konrod and C. Gotsman in the paper “Efficient Coding ofNon-Triangular Meshes,” Pacific Graphics Conference Proceedings,Hong-Kong, 2000; and A. Khodakovsky, P. Alliez, M. Desbrun, and P.Schroder in the paper “Near-Optimal Connectivity Encoding of 2-ManifoldPolygon Meshes,” Graphical Models, Special Issue on Processing of LargePolygonal Meshes, 2003. These algorithms focus on compressing theconnectivity information very efficiently, and are all based on atraversal of the primal or dual graph of the mesh. Some of them compressconnectivity of very regular meshes to a small fraction of a bit pervertex, and all to 2-4 bits per vertex in the worst case. When thegeometry information (vertex coordinates, and optionally normals,colors, and texture coordinates) is also taken into account, the costper vertex increases considerably. For example, adding only vertexcoordinates quantized to 10 bits per vertex lifts the cost to typically8-16 bits per vertex. In addition, all of these approaches areincompatible with the out-of-core nature of isosurface extractionalgorithms that visit the voxels in scan order.

In the paper “Progressive Geometry Compression,” Siggraph 2000Conference Proceedings, pages 271-278, July 2000, A. Khodakovsky, P.Schroder, and W. Sweldens follow a different approach to compress largeconnected and uniformly sampled meshes of low topological complexity,based on resampling, subdivision and wavelets. They obtain up to oneorder of magnitude better compression rates than with the connectivitypreserving schemes, by approximating the mesh geometry with asubdivision mesh, and compressing this mesh instead.

In the paper “Semi-Regular Mesh Extraction From Volumes,” IEEEVisualization 2000, Conference Proceedings, pages 275-282, October 2000,Z. J. Wood, M. Desbrun, P. Schroder, and D. Breen introduced a methodbased on surface wave propagation to extract isosurfaces from distancevolumes that produces semi-regular multi-resolution meshes. These meshescan be compressed with Khodakovsky's wavelet-based scheme.

Isosurface algorithms generally, take as input very large volume datafiles, and produce polygon meshes with very large number of vertices andfaces. Data stored in a server can be transmitted to a client for remotevisualization. The server can store and transmit the volume data to theclient, which then executes the isosurface algorithm on the receivedvolume data, and renders the resulting polygon mesh in a visualizationsystem. Alternatively, the server can compute the isosurface andtransmit the resulting polygon mesh to the client, which only rendersthe received polygon mesh in a visualization system.

In both cases the transmission time constitutes a major bottleneckbecause of the large file sizes involved. In the first case, in additionto the size of the transmitted data, the burden of the computation isshifted to the client. In the second case this is true even usinggeneral purpose polygon mesh compression schemes to reduce the size ofthe transmitted data. It is, therefore, important to compress the datastored in the server and/or transmitted to a remote client, and to beable to divide the computational burden between server and clientaccording to the computational resources of the client.

All isosurface construction algorithms construct an isosurfaceapproximation from an occupancy image, a set of intersection points, anda set of intersection point surface normals. The occupancy image, theset of intersection points, and the set of intersection point surfacenormals are extracted from the volume data. Since whether a grid edgeintersects the isosurface or not depends on the values of the scalarfunction at the grid edge ends, isosurface construction algorithmsgenerate polygon mesh vertices an faces as a function of an “occupancyimage” extracted from the volume data. The occupancy image is a 3Dbinary image defined by one grid vertex bit per grid vertexB={b _(α):α=(α₀,α₁,α₂)} where b _(α)ε{0,1},specifying whether the scalar function attains a value above or belowthe isovalue on that grid vertex. The location of the surface pointsalong the intersecting grid edges and the polygon mesh normals areassociated with the intersecting grid edges. A grid edge is anintersecting grid edge if occupancy image has different values at thegrid edge ends. Since the gradient vector of a function is normal to itslevel sets, normals used for shading can optionally be computed duringthe volume traversal as finite difference approximations to the gradientvectors normalized to unit length.

FIG. 2 is a flow chart of a typical prior art isosurface extractionalgorithm 240 which takes volume data 205 as input and produces surfacedata 220 as output. While the isosurface extraction algorithm 210 scansthe volume data in step 215, it determines the occupancy image in step230, computes the intersection points in step 235, computes normalvectors to the intersection points in step 240, and from the informationcontained in the occupancy image, intersection points, and normalvectors, in step 245 it computes a surface representation that returnsas the surface data 220.

FIG. 3 is a prior art diagram that shows the occupancy image 300composed of grid vertex bits 310, each grid vertex bit 310 correspondingto a grid vertex 320, each grid vertex 320 having an associated scalarfunction value 330, the value of the grid vertex bit 310 beingdetermined by whether the associated scalar function value 330 isgreater than the isovalue 340. In this diagram each grid points 320corresponds to a voxel 350 as in the Cuberille algorithm. The occupancyimage partitions the voxels into two sets 360 and 370. The topology andconnectivity of the isosurface 370 is determined by the set of voxelfaces separating the sets 360 and 370.

FIG. 4 is a prior art diagram that shows the intersection points. Eachintersection point 410 corresponds to one quadrilateral face 420separating the sets 360 and 370 of FIG. 3.

FIG. 5 is a prior art diagram that shows the normal vectors. Each normalvector 520 corresponds to one intersection point 510.

In the paper “Compression of Isosurfaces,” Proceedings of IEEE Vision,Modeling and Visualization (VMV 2001), Stuttgart, Germany, November2001, D. Saupe and J.-P. Kuska presented an algorithm to compressisosurfaces, which extracts and encodes the occupancy image andintersection points. Normals are computed from the reconstructedMarching Cubes polygon mesh. The occupancy image is encoded with anoctree-based scheme to deal more efficiently with large homogeneousregions of empty space. The intersection points are encoded with amulti-symbol context-based arithmetic coder. This is a complex methodwith compression rates significantly higher than those achieved usingthis invention. In the paper “Space-Efficient Boundary Representation ofVolumetric Objects,” Proceedings of the Joint Eurographics-IEEE TCVGSymposium on Visualization (VisSym01), Ascona, Switzerland, May 2001, L.Mroz and H. Hauser encode the occupancy image using a more complexscheme based on chain coding, where the voxels that contain isosurfaceintersections are linked in long chains and represented as a sequence ofsymbols, each one specifying in which direction to go to visit the nextcell. This method is also significantly less efficient than thisinvention, even if normals are not included in the compressed data. Inthe paper “Compressing Isosurfaces Generated with Marching Cubes,” TheVisual Computer, vol. 18, no. 1, pages 54-67, 2002, S. N. Yang and T. S.Wu describe a rather complex method to compress triangle meshesgenerated by the Marching Cubes algorithm. Each mesh vertex isrepresented by the index of the containing cube, the index of thesupporting edge, and the position of the vertex along the supportingedge. The decoder interconnects these vertices forming triangles usingthe occupancy image, as in the original Marching Cubes method. But theoccupancy image is not encoded in the bitstream. Instead, it isreconstructed from the cube and edge indices in the encoding of meshvertices by a complex procedure that in fact determines the connectedcomponents of the grid graph after removing the edges where meshvertices are supported. Normal vectors are not compressed. Compressionrates are several times worse than with the method of this invention,and it is not possible to do an out-of-core implementation.

Entropy encoding is a well established technique to represent with aminimum number of bits a finite sequence of “independent symbols” thatbelong to a finite “alphabet”. The fundamentals of entropy encoding isexplained by D. Salomon in the book “Data Compression: The CompleteReference,” Springer-Verlag, 1997, ISBN 0-387-98280-9. Symbols thatappear more often in the sequence are represented with fewer bits thanthose that appear more infrequently. The absolute lower bound for thetotal number of bits necessary to represent the sequence of independentsymbols with no loss of information is given by the so-called “entropy.”In practice the “arithmetic coder,” described by I. H. Witten, R. M.Neal, and J. G Cleary, in the paper “Arithmetic coding for datacompression,” Communications of the ACM, vol. 30, no. 6, June 1987,asymptotically achieves the entropy. Arithmetic coding is used as thebasis of many image and data compression schemes and applications, suchas those described by K. M. Marks, in the paper “A JBIG-ABIC compressionengine for digital document processing,” IBM Journal of Research andDevelopment, vol. 42, no. 6, 1998. Arithmetic coding has also beenimplemented in hardware, as described by M. J. Slattery and J. L.Mitchell, in the paper “The Qx-coder,” IBM Journal of Research andDevelopment, vol. 42, no. 6, 1998.

To deal with the lack of stationary distribution of symbols in thesequence, “adaptive” models are used. In arithmetic coding with anadaptive model the encoder updates the alphabet probabilities afterencoding each symbol. Since encoder and decoder must use the same modelto encode and decode each symbol, the model update procedure must bebased on data previously encoded, and agreed upon information. Amongthese data are the initial probabilities, which may be hard-coded orincluded in the compressed data. A common practice is to start withuniform probabilities and keep track of the relative symbol frequenciesas probability estimates.

For binary data, where the alphabet is composed of two symbols, keepingtrack of global symbol frequencies is usually not good enough as a modelupdate procedure, and a “context-based” procedure is used. This is astate machine model with separate sets of probability estimatesassociated with each state or “context”. The update procedure determinesthe context from previously encoded data, and after the symbol isencoded with the probabilities associated with a context, the set ofprobabilities corresponding to that context is updated, but not theother. Context-based arithmetic coding is a very efficient adaptivecompression scheme.

JBIG is short for “Joint Bi-level Image experts Group.” This is both thename of a standards committee, and of a particular scheme for thelossless compression of binary images, described in the internationalstandard ITU-T T.82 Information technology—Coded representation ofpicture and audio information—Progressive bi-level image compression,March 93. It can also be used for coding gray scale and color imageswith limited numbers of bits per pixel. JBIG is one of the bestavailable schemes for lossless image compression. The JBIG algorithm isbased on context-based arithmetic coding. For each pixel in an image a“context” is derived from a specific fixed pattern of surrounding pixelspreceding the current pixel in the scan order. The standard definesseveral such neighborhoods.

FIG. 6 is a prior art diagram showing two different ways 620 and 630 ofdefining a 10-bit context of a bit 610 described in the JBIG standard.All the above mentioned papers and references are incorporated hereinfor all purposes.

SUMMARY OF THE INVENTION

An aspect of this invention is provision of encoding systems and methodsfor compressing isosurface data.

A second aspect of this invention is provision of out-of-core decodingsystems and methods for decompression of compressed isosurface data.

A third aspect of this invention is provision of in-core decodingsystems and methods for decompression of compressed isosurface data.

Thus, this invention provides methods, apparatus and systems for a newand simple algorithm to compress isosurface data. This is the dataextracted by isosurface algorithms from scalar functions defined onvolume grids, and used to generate polygon meshes or alternativerepresentations. Isosurfaces are in widespread use in medical imaging,and scientific computation. The main features of this invention are itsextreme simplicity and high compression ratios, which are 5 to 25 timesbetter than those obtained with general purpose mesh compressionschemes.

In this algorithm the mesh connectivity and a substantial proportion ofthe geometric information are encoded to a fraction of a bit perMarching Cubes vertex with a context based arithmetic coder closelyrelated to the JBIG binary image compression standard. The remainingoptional geometric information, in the form of one quantized scalarvalue per intersecting grid edge, and specifying the location thecorresponding Marching Cubes vertex more precisely, is efficientlyencoded in scan-order with the same mechanism. Vertex normals canoptionally be computed as normalized gradient vectors by the encoder andincluded in the bitstream after quantization and entropy encoding, orcomputed by the decoder in a postprocessing smoothing step. Thesechoices are determined by tradeoffs associated with an in-core vs.out-of-core decoder structure.

An in-core isosurface decoder process produces a polygon mesh as asurface representation. This decoder process takes as input a compressedisosurface data with neither the optional intersection points record northe normal vectors record. In this decoder the normalized intersectionpoints are set to the default value one half, the normal vectors aregiven default values as a function of the neighboring intersection pointvalues. A subsequent smoothing algorithm is used as a global predictorto improve the quality of the reconstructed polygon mesh.

The out-of-core isosurface decoder process produces a set of orientedpoints as a surface representation. This decoder process takes as inputa compressed isosurface data with the optional intersection pointsrecord and the normal vectors record. Immediately after decoding andreconstructing each intersection point and corresponding normal vector,this decoder process generates one oriented point.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects, features, and advantages of the presentinvention will become apparent upon further consideration of thefollowing detailed description of the invention when read in conjunctionwith the drawing figures, in which:

FIG. 1 is a prior art diagram showing a 3D regular grid and one of itscells;

FIG. 2 is a flow chart of a typical prior art isosurface extractionalgorithm;

FIG. 3 is a prior art diagram that shows the occupancy image;

FIG. 4 is a prior art diagram that shows the intersection points;

FIG. 5 is a prior art diagram that shows the normal vectors;

FIG. 6 is a prior art diagram showing different ways of defining acontext of a bit described in the JBIG standard;

FIG. 7 is a block diagram showing an example computer system 700 onwhich an example of an advantageous embodiment of the present inventionoperates;

FIG. 8 is a flow chart describing the decomposition of an isosurfaceextraction algorithm into an encoder process and a decoder process;

FIG. 9 is a flow chart showing the steps of an example of anadvantageous embodiment of the isosurface encoder process;

FIG. 10 is a diagram describing an example of an advantageousimplementation of a step of the isosurface encoding process of FIG. 9,where the current context word is constructed combining occupancy bitscorresponding to previously visited grid vertices;

FIG. 11 is a diagram describing an example of an advantageousimplementation of two steps of the isosurface encoding process of FIG.9, where the location of an intersection point along its supporting gridedge is computed and encoded;

FIG. 12 is a flow chart showing the steps of an example of anadvantageous embodiment of the isosurface decoder process;

FIG. 13 is a diagram that shows the use of a smoothing algorithm as aglobal predictor to improve the quality of a reconstructed polygon mesh;

FIG. 14 is a flow chart of an in-core more advantageous embodiment ofthe isosurface decoder process of FIG. 12, which produces a polygon meshas a surface representation; and

FIG. 15 is a flow chart of an out-of-core more advantageous embodimentof the isosurface decoder process of FIG. 12, which produces a set oforiented points as a surface representation.

DETAILED DESCRIPTION OF THE INVENTION

This invention provides systems, structures, apparatus and methods for‘Bi-level iso-surface compression’, (BLIC). It provides encoding systemsand methods for compressing isosurface data, out-of-core decodingsystems and methods for decompression of compressed isosurface data, andin-core decoding systems and methods for decompression of compressedisosurface data.

An encoder process takes volume data and an isolevel as input andproduces compressed isosurface data as output. The volume datacomprising the values of a scalar function evaluated at the gridvertices of a 3D regular grid. The 3D regular grid also having gridedges, with each grid edge having two neighboring grid vertices as edgeends. The volume data being organized as layers, rows, and columns. Thecompressed isosurface data including sufficient information toreconstruct a surface approximation to the level set of the scalarfunction associated with the isolevel in the volume spanned by the 3Dregular grid. The compressed isosurface data produced by the encoderprocess is composed of an occupancy image record, an optionalintersection points record, and an optional normal vectors record. Theoccupancy image record including a compressed occupancy image. Theoccupancy image being a binary image with values corresponding to thegrid vertices of the 3D regular grid and determined by thresholding thevalues of the scalar function at the vertices of the 3D regular gridwith respect to the isovalue. The occupancy image compressed with acontext-based arithmetic encoder. Each current grid vertex encoded withrespect to a current context word. The context word being a binary wordwith a finite number of bits. The bits of the binary word beingdetermined by preceding neighboring values of the occupancy imagecorresponding to grid vertices that precede and are neighbors of thecurrent grid vertex in the scan order. The preceding neighboring valuesbelonging to one or more layers, one or more rows, and one or morecolumns of the volume data. The optional intersection points recordincluding a set of normalized intersection parameters. Each normalizedintersection parameter being a number between zero and one, andspecifying the location of a corresponding intersection point along acorresponding intersection edge. The intersection edges being gridedges. A grid edge being an intersection edge if the values of theoccupancy image corresponding to its ends are different. The optionalnormal vectors record including a set of compressed intersection pointnormal vectors. Each intersection point normal vector computed from thevolume data.

The compressed isosurface data can be stored in a data storage device ortransmitted through a network or other communication medium to a remotecomputer system, where the decoder process is executed. The decoderprocesses take compressed surface data as input and produce surface dataas output. The decoder processes first reconstructs the occupancy imageby decoding the occupancy image record. The decoder processes thendetermines the intersection edges and either decodes the intersectionpoints and corresponding normal vectors from the intersection pointsrecord and normal vectors record, respectively, if present in thecompressed isosurface data. Otherwise the decoder process assignsdefault values to the intersection points and corresponding normalvectors.

The in-core isosurface decoder process produces a polygon mesh as asurface representation. This decoder process takes as input a compressedisosurface data with neither the optional intersection points record northe normal vectors record. In this decoder the normalized intersectionpoints are set to the default value one half, the normal vectors aregiven default values as a function of the neighboring intersection pointvalues. A subsequent smoothing algorithm is used as a global predictorto improve the quality of the reconstructed polygon mesh.

The out-of-core isosurface decoder process produces a set of orientedpoints as a surface representation. This decoder process takes as inputa compressed isosurface data with the optional intersection pointsrecord and the normal vectors record. Immediately after decoding andreconstructing each intersection point and corresponding normal vector,this decoder process generates one oriented point.

FIG. 7 is a block diagram showing an example of a computer system 700 onwhich an example of an advantageous embodiment of the present inventionoperates. The advantageous embodiment includes one or more applicationprograms 702. One type of application program 702 is a compiler 705,which includes an optimizer 706. The compiler 705 and optimizer 706 areconfigured to transform a source program into optimized executable code.More generally, the source program is transformed to an optimized formand then into executable code. The compiler 705 and optimizer 706operate on a computer platform 704 that includes a hardware unit 712.Some application programs 702 that run on the system 700 include theisosurface encoder method 810, and the isosurface decoder method 820.

FIG. 8 is a flow chart describing the decomposition of an isosurfaceextraction algorithm into an encoder process 810 and a decoder process820. The encoder process 810 takes volume data 805 as input and producescompressed isosurface data 815 as output The decoder process 812 takescompressed surface data 815 as input and produces surface data 825 asoutput. The compressed isosurface data 815 comprises an occupancy imagerecord 816, an optional intersection points record 817, and an optionalnormal vectors record 818. The compressed isosurface data 815 can bestored in a data storage device 730 or transmitted through a network orother communication medium to a remote computer system 700, where thedecoder process 820 is executed. While the encoder process 810 scans thevolume data in steps 830, it detennines the occupancy image in step 840,computes the intersection points in step 850, and computes theintersection point normals in step 860. In step 870 the decoder process820 constructs a surface representation as function of the compresseddata 815, which outputs as surface data 825. The intersection pointsrecord 817 and the normal vectors record 818 are optional components ofthe compressed isosurface data 815.

FIG. 9 is a flow chart showing the steps of an example of anadvantageous embodiment of the isosurface encoder process 810 of FIG. 8.While scanning the volume data in scan order, the method extracts theoccupancy image 816, the set of intersection points 817, and the set ofintersection point surface normals 818. The isosurface encoder processcomprises three loops. Steps 205 and 295 are the beginning and end of anouter loop over the layers of the volume data. Steps 210 and 290 are thebeginning and end of a middle loop over the rows of the volume data.Steps 215 and 285 are the beginning and end of an inner loop over thecolumns of the volume data. Inside the inner loop, in step 220 a currentoccupancy bit is determined by comparing a corresponding scalar functionvalue with the isovalue. In step 225 a current context word isconstructed combining occupancy bits corresponding to grid verticespreviously visited. In step 230 the current occupancy bit is encodedwith respect to the current context. For each grid vertex there areexactly three other grid vertices, which are neighbors of the gridvertex and precede the grid vertex in the scan order. Steps 235 and 280are the beginning and end of a fourth loop that allows the algorithm toconsider each one of the three other grid vertices and the edges joiningthose grid vertices with the grid vertex in sequence. In step 240 thecurrent occupancy bit is compared with the occupancy bit correspondingto the previously visited neighbor grid vertex to determine if anintersection point exists along the edge connecting the current gridvertex and the previously visited grid vertex. If the values aredifferent in step 250 the location of the intersection point along theedge is computed. In step 255 the location of the intersection point isencoded into intersection points record 817 of the compressed data 815.In step 260 a normal vector corresponding to the intersection point iscomputed as function of the volume data. In step 265 the normal vectorcorresponding to the intersection point is encoded into normal vectorsrecord 818 of the compressed data 815. Steps 235, 240, 250, 255, 260,265, 275, and 280 are optional. An embodiment implemented without thesesteps produces a compressed isosurface data 815 without the optionalrecords 817 and 818.

FIG. 10 is a diagram describing an example of an advantageousimplementation of step 225 of the isosurface encoding process 810 ofFIG. 9, where the current context word is constructed combiningoccupancy bits corresponding to previously visited grid vertices. Thelocation of the current grid vertex is defined by a current layer 1010,a current row 1020, and a current column 1030. The current layer 1010 ispreceded by a previous layer 1015. The current row 1020 is preceded by aprevious row 1025. The current column 1030 is preceded by a previouscolumn 1035. Exactly seven other grid vertices precede the current gridvertex in the scan order. These seven other grid vertices are supportedby the current or previous layer, the current or previous row, and thecurrent or previous column. The current context word is a seven bit wordconstructed concatenating the values of the occupancy bits correspondingto the seven other grid vertices in scan order.

FIG. 11 is a diagram describing an example of an advantageousimplementation of steps 250 and 255 of the isosurface encoding process810 of FIG. 9, where the location of an intersection point 1110 alongits supporting grid edge is computed and encoded. The location of theintersection point 1110 along its supporting edge is described by anormalized intersection point parameter 1120, which is a number neitherless than zero nor greater than one. This number is quantized to afinite number of bits and entropy encoded in step 255.

FIG. 12 is a flow chart showing the steps of an example of anadvantageous embodiment 1200 of the isosurface decoder process 820 ofFIG. 8. This advantageous embodiment can decode the compressedisosurface data 815 produced by the isosurface encoder process 810 withor without the optional records 817 and 818. While scanning the volumedata in scan order, the method decodes the occupancy image, theintersection points, and the intersection point surface normals. Thisembodiment can produce either a polygon mesh or a set of oriented pointsas output surface representation. If producing a polygon mesh as outputsurface representation, from the information included in the occupancyimage the method generates in step 1230 the topology and connectivity ofthe reconstructed polygon mesh. If producing a set of oriented points asoutput surface representation, step 1230 is not performed. From thelocation of the intersection points and the intersection point normals,the method reconstructs the geometry of the surface representation. Theisosurface decoder process comprises three loops. Steps 1205 and 1295are the beginning and end of an outer loop over the layers of the volumedata. Steps 1210 and 1290 are the beginning and end of a middle loopover the rows of the volume data. Steps 1215 and 1285 are the beginningand end of an inner loop over the columns of the volume data. Inside theinner loop, in step 1220 a current context word is constructed combiningoccupancy bits corresponding to grid vertices previously visited. Instep 1225 a current occupancy bit is decoded from the occupancy imagerecord 816 of the compressed isosurface data 815 with respect to thecurrent context. For each grid vertex there are exactly three other gridvertices, which are neighbors of the grid vertex and precede the gridvertex in the scan order. Steps 1235 and 1280 are the beginning and endof a fourth loop that allows the algorithm to consider each one of thethree other grid vertices and the edges joining those grid vertices withthe grid vertex in sequence. Steps 1240 and 1275 are the beginning andend of an if statement, respectively, in which the current occupancy bitis compared with the occupancy bit corresponding to the previouslyvisited neighbor grid vertex to determine if an intersection pointexists along the edge connecting the current grid vertex and thepreviously visited grid vertex. If the values are different in step 1250the location of the intersection point along the edge is determined. Ifthe compressed isosurface data includes an intersection points record817, then the value of the normalized intersection point parameter isdecoded from the intersection points record 817. If the compressedisosurface data does not include an intersection points record 817, thenthe normalized intersection point parameter is set to a default value.In an example of an advantageous implementation this default value isequal to one half. In step 1260 a normal vector corresponding to theintersection point is determined. If the compressed isosurface dataincludes a normal vectors record 818, then the normal vector is decodedfrom the normal vectors record 818. If the compressed isosurface datadoes not include an normal vectors record 818,then intersection pointnormal vector is set to a default value. Tin an example of anadvantageous implementation this default value is one of the sixorientations determined by the three coordinate axes. In an example ofan advantageous embodiment an additional geometry smoothing step 1297 isperformed to improved the quality of the reconstructed surfacerepresentation.

FIG. 13 is a diagram that shows the use of a smoothing algorithm as aglobal predictor to improve the quality of a reconstructed polygon mesh.The smoothing algorithm is applied to the polygon mesh 1310reconstructed by steps 1205 to 1295 of the method of FIG. 12, producinga smoother polygon mesh 1320.

FIG. 14 is a flow chart of an in-core more advantageous embodiment 1400of the isosurface decoder process of FIG. 12, which produces a polygonmesh as a surface representation. This advantageous implementation takesas input a compressed isosurface data 815 with neither the optionalintersection points record 817 nor the normal vectors record 818. Inthis embodiment step 1410 replaces step 1250 of the flow chart 1200. Instep 1410 the normalized intersection point parameter is set to thedefault value one half. In step 1420 the normal vector corresponding tothe intersection point is given a default value as a function of theneighboring intersection point values. In this advantageous embodimentthe smoothing step 1297 is mandatory to improve the quality of thereconstructed polygon mesh.

FIG. 15 is a flow chart of an out-of-core more advantageous embodiment1500 of the isosurface decoder process of FIG. 12, which produces a setof oriented points as a surface representation. This advantageousimplementation takes as input a compressed isosurface data 815 with theoptional intersection points record 817 and the normal vectors record818. After step 1260 this advantageous embodiment has the additionalstep 1510 of generating one oriented point. The output surfacerepresentation is the set of oriented points generated in step 1510.

Thus the present invention includes a data structure comprising, amemory of a computer system storing the data structure for representingan isosurface polygonal mesh, the isosurface polygonal meshapproximating a level set of a scalar function, the scalar functiondefined by function values and a regular three-dimensional grid, thelevel set defined by an isolevel, each function value associated with anode of the regular three-dimensional grid, the data structure having anoccupancy record, the occupancy record including a three-dimensionaloccupancy image, the three-dimensional occupancy image composed ofoccupancy bits, each occupancy bit associated with a node of thethree-dimensional grid, each occupancy bit being equal to either a firstvalue or a second value, each occupancy bit having a correspondingfunction value, each occupancy bit being equal to the first value if thecorresponding function value is less than the isolevel, and to thesecond value if the corresponding function value is higher than theisolevel.

In some embodiments of the data structure, the occupancy image iscompressed using a context-based arithmetic coder, the context basedarithmetic coder encoding the occupancy bit in a scanning order, thecontext-based arithmetic associating a context word to each occupancybit, the context word composed of context word bits, each context wordbit being a preceding occupancy bit, the preceding occupancy bitspreceding the occupancy bits in the scanning order; and/or the pointlocation values are numbers between zero and one; and/or the pointlocation values are quantized; and/or the point location values arecompressed; and/or the quantized location values are represented as oneor more point bitplane three-dimensional images, and each point bitplanethree-dimensional image is compressed using a context-based arithmetic;and/or the normal vectors are quantized into quantized normal vectors;and/or the normal vectors are compressed; and/or the quantized normalvectors are represented as one or more normal bitplane three-dimensionalimages, and each normal bitplane three-dimensional image is compressedusing a context-based arithmetic coder.

In some embodiments of the data structure, the structure furthercomprises: an intersection record, the intersection record composed ofpoint location values, each point location value associated with anintersecting grid edge, each intersecting grid edge having two edgeends, the edge ends being grid nodes, the two grid nodes being neighborsin the three-dimensional grid, the occupancy bits corresponding to thetwo grid nodes having different values; and/or a normal vector record,the normal vector record being composed of normal vectors, each normalvector being associated with an intersecting grid edge.

The invention also includes a compression method comprising: determiningvalues of occupancy bits of an occupancy image as a function of athree-dimensional grid, a scalar function and an isolevel, thecompression method visiting the nodes of the three-dimensional grid inthe scanning order, comparing the function value associated with eachnode with the isolevel, setting a value of the occupancy bit associatedwith the node to a first value if the function value is less than theisolevel, and to a second value if the function value is higher than theisolevel. In some embodiments of the compression method, the methodfurther comprising determining the point location values; and/ordetermining the normal vector values.

The invention also includes a decompression method comprisingreconstructing an isosurface polygon mesh from an occupancy image. Themethod having steps outlined above and known to those skilled in theart.

The invention also includes a system comprising, a memory of a computersystem storing the data structure for representing an isosurfacepolygonal mesh, the isosurface polygonal mesh approximating a level setof a scalar function, the scalar function defined by function values anda regular three-dimensional grid, the level set defined by an isolevel,each function value associated with a node of the regularthree-dimensional grid, the data structure having an occupancy record,the occupancy record including a three-dimensional occupancy image, thethree-dimensional occupancy image composed of occupancy bits, eachoccupancy bit associated with a node of the three-dimensional grid, eachoccupancy bit being equal to either a first value or a second value,each occupancy bit having a corresponding function value, each occupancybit being equal to the first value if the corresponding function valueis less than the isolevel, and to the second value if the correspondingfunction value is higher than the isolevel.

The invention also includes a method comprising: storing a datastructure for representing an isosurface polygonal mesh, the isosurfacepolygonal mesh approximating a level set of a scalar function, thescalar function defined by function values and a regularthree-dimensional grid, the level set defined by an isolevel, eachfunction value associated with a node of the regular three-dimensionalgrid; providing the data structure with an occupancy record, theoccupancy record including a three-dimensional occupancy image, thethree-dimensional occupancy image composed of occupancy bits, eachoccupancy bit associated with a node of the three-dimensional grid, eachoccupancy bit being equal to either a first value or a second value,each occupancy bit having a corresponding function value; and settingeach occupancy bit being equal to the first value if the correspondingfunction value is less than the isolevel, and to the second value if thecorresponding function value is higher than the isolevel.

The invention also includes a system comprising: a memory of a computersystem storing the data structure for representing an isosurfacepolygonal mesh, the isosurface polygonal mesh approximating a level setof a scalar function, the scalar function defined by function values anda regular three-dimensional grid, the level set defined by an isolevel,each function value associated with a node of the regularthree-dimensional grid, the data structure having an occupancy record,the occupancy record including a three-dimensional occupancy image, thethree-dimensional occupancy image composed of occupancy bits, eachoccupancy bit associated with a node of the three-dimensional grid, eachoccupancy bit being equal to either a first value or a second value,each occupancy bit having a corresponding function value, each occupancybit being equal to the first value if the corresponding function valueis less than the isolevel, and to the second value if the correspondingfunction value is higher than the isolevel.

The invention also includes a method comprising: storing a datastructure for representing an isosurface polygonal mesh, the isosurfacepolygonal mesh approximating a level set of a scalar function, thescalar function defined by function values and a regularthree-dimensional grid, the level set defined by an isolevel, eachfunction value associated with a node of the regular three-dimensionalgrid, providing the data structure with an occupancy record, theoccupancy record including a three-dimensional occupancy image, thethree-dimensional occupancy image composed of occupancy bits, eachoccupancy bit associated with a node of the three-dimensional grid, eachoccupancy bit being equal to either a first value or a second value,each occupancy bit having a corresponding function value, setting eachoccupancy bit being equal to the first value if the correspondingfunction value is less than the isolevel, and to the second value if thecorresponding function value is higher than the isolevel.

The invention also includes an article of manufacture comprising acomputer usable medium having computer readable program code meansembodied therein for causing data compression, the computer readableprogram code means in said article of manufacture comprising computerreadable program code means for causing a computer to effect the stepsof any method of this invention.

The invention also includes a program storage device readable bymachine, tangibly embodying a program of instructions executable by themachine to perform method steps for data compression, said method stepscomprising the steps of any method of this invention.

The invention also includes a computer program product comprising acomputer usable medium having computer readable program code meansembodied therein for causing formation of a data structure, the computerreadable program code means in said computer program product comprisingcomputer readable program code means for causing a computer to effectthe functions of the present invention.

Thus, the present invention can be realized in hardware, software, or acombination of hardware and software. A visualization tool according tothe present invention can be realized in a centralized fashion in onecomputer system, or in a distributed fashion where different elementsare spread across several interconnected computer systems. Any kind ofcomputer system—or other apparatus adapted for carrying out the methodsand/or functions described herein—is suitable. A typical combination ofhardware and software could be a general purpose computer system with acomputer program that, when being loaded and executed, controls thecomputer system such that it carries out the methods described herein.The present invention can also be embedded in a computer programproduct, that comprises all the features enabling the implementation ofthe methods described herein, and that—when loaded in a computersystem—is able to carry out these methods.

Computer program means or computer program in the present contextinclude any expression, in any language, code or notation, of a set ofinstructions intended to cause a system having an information processingcapability to perform a particular function either directly or afterconversion to another language, code or notation, and/or reproduction ina different material form.

Thus the invention includes an article of manufacture that comprises acomputer usable medium having computer readable program code meansembodied therein for causing a function described above. The computerreadable program code means in the article of manufacture comprisescomputer readable program code means for causing a computer to effectthe steps of a method of this invention. Similarly, the presentinvention may be implemented as a computer program product comprising acomputer usable medium having computer readable program code meansembodied therein for causing a function described above. The computerreadable program code means in the computer program product comprisingcomputer readable program code means for causing a computer to effectone or more functions of this invention. Furthermore, the presentinvention may be implemented as a program storage device readable bymachine, tangibly embodying a program of instructions executable by themachine to perform method steps for causing one or more functions ofthis invention.

It is noted that the foregoing has outlined some of the more pertinentobjects and embodiments of the present invention. This invention may beused for many applications. Thus, although the description is made forparticular arrangements, timing indications and methods, the intent andconcept of the invention is suitable and applicable to otherarrangements and applications. It will be clear to those skilled in theart that modifications to the disclosed embodiments can be effectedwithout departing from the spirit and scope of the invention. Thedescribed embodiments ought to be construed to be merely illustrative ofsome of the more prominent features and applications of the invention.Other beneficial results can be realized by applying the disclosedinvention in a different manner or modifying the invention in ways knownto those familiar with the art.

1. A computer system comprising a memory, a data structure stored in thememory of the computer system for representing an approximateisosurface, the approximate isosurface approximating a level set of ascalar function, the scalar function defined by function values and a 3Dregular grid, the 3D regular grid comprising a plurality of gridvertices and a plurality of grid edges, each grid edge having two edgeends, each edge end being a grid vertex, the level set defined by anisolevel, each function value corresponding to one grid vertex of the 3Dregular grid, the data structure embodied in computer-readable materialused in at least one of a computer graphics application and scientificvisualization application to representing isosurface data in compressedform, and having mesh connectivity and a substantial first proportion ofgeometric information encoded to a fraction of a bit per Marching Cubesvertex with a context based arithmetic coder, and having any remainingsecond proportion of geometric information in the form of one quantizedscalar value per intersecting grid edge, and specifying the location thecorresponding Marching Cubes vertex more precisely, being efficientlyencoded in scan-order with the same mechanism, the data structurecomprising: an occupancy image record, the occupancy image recordincluding an encoded occupancy image, the encoded occupancy image beingthe result of applying a binary encoding algorithm to an existingoccupancy image, the existing occupancy image composed of occupancybits, each occupancy bit corresponding with the grid vertex of the 3Dregular grid, each occupancy bit being equal to one of a first value anda second value, and each occupancy bit having a corresponding functionvalue, each occupancy bit being equal to the first value if thecorresponding function value is less than the isolevel, and to thesecond value if the corresponding function value is higher than theisolevel.
 2. A computer system as recited in claim 1, wherein the binaryencoding algorithm is a context-based arithmetic coder, the contextbased arithmetic coder encoding the bits of the occupancy image in ascanning order, the context-based arithmetic coder using a differentcontext word to encode each current bit of the occupancy image, thecontext word composed of context word bits, each context word bit beingequal to a preceding occupancy bit, and the preceding occupancy bitbeing a bit of the occupancy image preceding the current bit in thescanning order.
 3. A computer system as recited in claim 1, furthercomprising: an intersection points record, the intersection pointsrecord composed of normalized intersection parameters, each normalizedintersection parameter associated with an intersecting grid edge, eachintersecting grid edge having two edge ends, each edge end being one ofthe grid vertices, wherein two grid nodes being neighbors in the 3Dregular grid, the occupancy bits corresponding to the two grid nodeshaving different values.
 4. A computer system as recited in claim 3,wherein the normalized intersection parameters are numbers between zeroand one.
 5. A computer system as recited in claim 4, wherein thenormalized intersection parameters are quantized.
 6. A computer systemas recited in claim 5, wherein the normalized intersection parametersare compressed.
 7. A computer system as recited in claim 5, wherein thequantized normalized intersection parameters are represented as one ormore point bitplane three-dimensional images, and each point bitplanethree-dimensional image is compressed using the context-based arithmeticcoder.
 8. A computer system as recited in claim 1, further comprising anormal vector record, the normal vector record composed of normalvectors, each normal vector associated with the intersecting grid edge.9. A computer system as recited in claim 8, wherein the normal vectorsare quantized.
 10. A computer system as recited in claim 8, wherein thenormal vectors are compressed.
 11. A computer system as recited in claim9, wherein the quantized normal vectors are represented as one or morenormal bitplane three-dimensional images, and each normal bitplanethree-dimensional image is compressed using a context-based arithmeticcoder.
 12. An encoding method comprising: determining values ofoccupancy bits of an occupancy image as a function of a 3D regular grid,a scalar function and an isolevel, the occupancy image embodied incomputer-readable material for use in at least one of a computergraphics application and a scientific visualization application torepresent isosurface data in compressed form, and having meshconnectivity and a substantial first proportion of geometric informationencoded to a fraction of a bit per Marching Cubes vertex with a contextbased arithmetic coder, and having any remaining second proportion ofgeometric information in the form of one quantized scalar value perintersecting grid edge, and specifying the location the correspondingMarching Cubes vertex more precisely, being efficiently encoded inscan-order with the same mechanism, the method further comprising:visiting the nodes of the three-dimensional grid in a scanning order,visiting the nodes of the three-dimensional grid in a scanning order,comparing the function value associated with each node with theisolevel, setting a value of the occupancy bit associated with each nodeto a first value if the function value is less than the isolevel,setting the value of the occupancy bit associated with each node to asecond value if the function value is higher than the isolevel, andemploying the occupancy bit value associated with each node in saidoccupancy image embodied in said computer-readable material for use insaid at least one of said computer graphics application and saidscientific visualization application to represent isosurface data incompressed form.
 13. A method as recited in claim 12, further comprisingdetermining the point location values.
 14. A method as recited in claim12, further comprising determining the normal vector values.
 15. Anarticle of manufacture comprising a computer readable medium havingcomputer readable program code means embodied therein for causing datacompression, the computer readable program code means in said article ofmanufacture comprising computer readable program code means for causinga computer to effect the steps of claim
 12. 16. A program storage devicereadable by a computer, tangibly embodying a program of instructionsexecutable by the computer to perform method steps for data compression,said method steps comprising the steps of claim
 12. 17. A decodingmethod comprising reconstructing an isosurface polygon mesh from anoccupancy image, comprising the steps of: taking compressed surface dataas input and producing surface data as output, said mesh having meshconnectivity and a substantial first proportion of geometric informationencoded to a fraction of a bit per Marching Cubes vertex with a contextbased arithmetic coder, and having any remaining second proportion ofgeometric information in the form of one quantized scalar value perintersecting grid edge, and specifying the location the correspondingMarching Cubes vertex more precisely, being efficiently encoded inscan-order with the same mechanism; reconstructing the occupancy imageby decoding an occupancy image record; determining intersection edgesand decoding intersection points and corresponding normal vectors froman intersection points record and an normal vectors record,respectively, if present in the compressed isosurface data; assigningdefault values to the intersection points and corresponding normalvectors, if the intersection points record and normal vectors record arenot present in the compressed isosurface data, and employing results ofthe steps of reconstructing, determining and assigning in said occupancyimage embodied in a computer-readable material for use in at least oneof a computer graphics application and a scientific visualizationapplication to represent the isosurface data.
 18. A method comprising anin-core isosurface decoder process embodied in computer-readablematerial producing a polygon mesh as a surface representation, said meshhaving mesh connectivity and a substantial first proportion of geometricinformation encoded to a fraction of a bit per Marching Cubes vertexwith a context based arithmetic coder, and having any remaining secondproportion of geometric information in the form of one quantized scalarvalue per intersecting grid edge, and specifying the location thecorresponding Marching Cubes vertex more precisely, being efficientlyencoded in scan-order with the same mechanism, the process including:taking as input compressed isosurface data without an optionalintersection points record and without a normal vectors record; settingnormalized intersection points to a default value of one half, givingnormal vectors default values being a function of neighboringintersection point values; using a smoothing algorithm as a globalpredictor to form and improve a quality of a reconstructed polygon mesh,and employing results of the steps of setting, giving and using inproducing said polygon mesh as said surface representation, embodied insaid computer-readable material for use in at least one of a computergraphics application and a scientific visualization application.
 19. Amethod as recited in claim 18, further comprising at least one ofstoring compressed isosurface data in a data storage device;transmitting the compressed isosurface data through a communicationmedium to a remote computer system wherein the process is executed. 20.A method as recited in claim 18, including reconstructing the polygonmesh from an occupancy image.
 21. A program storage device readable by acomputer, tangibly embodying a program of instructions executable by thecomputer to perform method steps for data decompression, said methodsteps comprising the steps of claim
 18. 22. An article of manufacturecomprising a computer readable medium having computer readable programcode means embodied therein for causing data control, the computerreadable program code means in said article of manufacture comprisingcomputer readable program code means for causing a computer to effectthe steps of claim
 19. 23. A method comprising an out-of-core isosurfacedecoder process producing a set of oriented points as a surfacerepresentation, the process including: taking as input compressedisosurface data with any optional intersection points record and anyoptional normal vectors record; generating one oriented point afterdecoding and reconstructing each said any optional intersection pointand corresponding said any optional normal vector, and employing resultsof the steps of taking and generating in producing said set of orientedpoints as said surface representation, embodied in a computer-readablematerial for use in at least one of a computer graphics application anda scientific visualization application; and reconstructing an isosurfacepolygon mesh from said set of oriented points as a surfacerepresentation, said mesh having mesh connectivity and a substantialfirst proportion of geometric information encoded to a fraction of a bitper Marching Cubes vertex with a context based arithmetic coder, andhaving any remaining second proportion of geometric information in theform of one quantized scalar value per intersecting grid edge, andspecifying the location the corresponding Marching Cubes vertex moreprecisely, being efficiently encoded in scan-order with the samemechanism.
 24. A system comprising: a memory of a computer systemstoring the data structure for representing an isosurface polygonal meshand having mesh connectivity and a substantial first proportion ofgeometric information encoded to a fraction of a bit per Marching Cubesvertex with a context based arithmetic coder, and having any remainingsecond proportion of geometric information in the form of one quantizedscalar value per intersecting grid edge, and specifying the location thecorresponding Marching Cubes vertex more precisely, being efficientlyencoded in scan-order with the same mechanism, the isosurface polygonalmesh approximating a level set of a scalar function, the scalar functiondefined by function values and a regular three-dimensional grid, thelevel set defined by an isolevel, each function value associated with anode of the regular three-dimensional grid, the data structure having anoccupancy record, the occupancy record including a three-dimensionaloccupancy image, the three-dimensional occupancy image composed ofoccupancy bits, each occupancy bit associated with a node of thethree-dimensional grid, each occupancy bit being equal to either a firstvalue or a second value, each occupancy bit having a correspondingfunction value, each occupancy bit being equal to the first value if thecorresponding function value is less than the isolevel, and to thesecond value if the corresponding function value is higher than theisolevel.
 25. A method comprising: storing a data structure forrepresenting an isosurface polygonal mesh, and having mesh connectivityand a substantial first proportion of geometric information encoded to afraction of a bit per Marching Cubes vertex with a context basedarithmetic coder, and having any remaining second proportion ofgeometric information in the form of one quantized scalar value perintersecting grid edge, and specifying the location the correspondingMarching Cubes vertex more precisely, being efficiently encoded inscan-order with the same mechanism, the isosurface polygonal meshapproximating a level set of a scalar function, the scalar functiondefined by function values and a regular three-dimensional grid, thelevel set defined by an isolevel, each function value associated with anode of the regular three-dimensional grid, providing the data structurewith an occupancy record, the occupancy record including athree-dimensional occupancy image, the three-dimensional occupancy imagecomposed of occupancy bits, each occupancy bit associated with a node ofthe three-dimensional grid, each occupancy bit being equal to either afirst value or a second value, each occupancy bit having a correspondingfunction value, setting each occupancy bit being equal to the firstvalue if the corresponding function value is less than the isolevel, andto the second value if the corresponding function value is higher thanthe isolevel, and employing each occupancy bit value in said occupancyimage embodied in a computer-readable material for use in at least oneof a computer graphics application and a scientific visualizationapplication to represent isosurface data.
 26. An encoding apparatuscomprising: means for determining values of occupancy bits of anoccupancy image as a function of a 3D regular grid, a scalar functionand an isolevel, and having mesh connectivity and a substantial firstproportion of geometric information encoded to a fraction of a bit perMarching Cubes vertex with a context based arithmetic coder, and havingany remaining second proportion of geometric information in the form ofone quantized scalar value per intersecting grid edge, and specifyingthe location the corresponding Marching Cubes vertex more precisely,being efficiently encoded in scan-order with the same mechanism, themeans including: means for visiting nodes of the three-dimensional gridin scanning order, means for comparing a function value associated witheach node with the isolevel, means for setting a value of the occupancybit associated with each node to a first value if the function value isless than the isolevel, and means for setting the value of the occupancybit associated with each node to a second value if the function value ishigher than the isolevel.